Factor the following expression: $8$ $x^2+$ $37$ $x+$ $20$
Explanation: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(8)}{(20)} &=& 160 \\ {a} + {b} &=& & & {37} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $160$ and add them together. The factors that add up to ${37}$ will be your ${a}$ and ${b}$ When ${a}$ is ${5}$ and ${b}$ is ${32}$ $ \begin{eqnarray} {ab} &=& ({5})({32}) &=& 160 \\ {a} + {b} &=& {5} + {32} &=& 37 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {8}x^2 +{5}x +{32}x +{20} $ Group the terms so that there is a common factor in each group: $ ({8}x^2 +{5}x) + ({32}x +{20}) $ Factor out the common factors: $ x(8x + 5) + 4(8x + 5) $ Notice how $(8x + 5)$ has become a common factor. Factor this out to find the answer. $(8x + 5)(x + 4)$